copy the size and scale a texture is mapped by, from one object to another
Very big difference of UV maps 

UV map of the "Object A" looks like this:



Note: it's scaled up very much; texture space isn't seen here, but it's located where the cursor is placed.

UV map of the "Object B" is this:



It's not scaled as much as the first one, and it's unwrapped not in the same manner. For the first object Project from View probably used (and no seams on the mesh), while some other method used for "Object B".
Thus the objects definitely won't look the same.

Make one object look like another

What you should try is to unwrap and scale UV maps of both objects roughly in the same way; then you'll be ready to assign the same material for the objects (or creating new one).

Possible solution


Enter orthographic mode (Numpad 1). Select "Object B", enter Edit mode, select all.
Use U > Project From View. 
Open UV/Image Editor to scale and position UV map in adjacent way (it depends on texture, but most likely you won't need to rotate it). Make the scale of UV map so it to fit the texture space (it may be eaiser to setup mapping settings then).
Set the Size in the Mapping scroll of the texture settings to something like 50 (for X and Y axes). This is intended to substitute scaling UV map; while it does roughly the same, it's simply easier to control the UV map which has size of texture space in UV/Image Editor. To adjust scale just tweak that Size parameter.